Mooring Forces Port or STBD On Quay WWW - Thenavalarch.com Rev 1 [PDF]

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MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



Mooring Forces Calculator (Port or Starboard on Quay) www.thenavalarch.com What does this Excel Sheet do? This Excel sheet helps you calculate the environmental forces on a vessel when it is moored by Port or Starboard Side aligned with the Quay (as shown in figure on right) It further calculates the Line Tensions on the Mooring Lines, and reports the Factor of Safety for each mooring line How to use this Excel Sheet The user is asked for some inputs for the Vessel, Cargo and Environment and Mooring Line Configuration. The Input cells are highlighted in blue. The user has to provide all the inputs highlighted in blue. Please do not make any changes to the output sheets For some inputs, Tables and charts are required to be referred. These Tables and charts are provided alongwith for the user to enter these inputs. Once all inputs are provided, the Environmental forces are calculated, and from these forces, the Mooring Line Tensions are calculated The user should conduct separate checks for normal and heavy weather conditions. Factors of safety are 9.0 for normal, and 3.0 for heavy weather condition The mooring pattern should be investigated for both ballast and fully loaded cases for each weather condition Coordinate System and Axes (See figure on right) The origin of coordinate system is at fwd end of the vessel longitudinally, Centreline transversely and at Mean Sea Level vertically X-axis is positive towards aft, Y-axis is positive towards the quay, Z-axis is positive vertically upwards Assumptions/Limitations Mooring line arrangement should be symmetrical about the midship of the vessel Wind and current forces are assumed to be steady state in nature. Wave force is assumed to be negligible The line spring coefficients are constant, i.e., the Cyoung's modulus of mooring lines does not vary much with line tension forces References 1. DDS-582-1 Calculations for Mooring Systems, Department of the Navy, Naval Sea Systems Command, Washington DC, 20362-5101



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MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



MOORING FORCES CALCULATION - VESSEL INPUTS



General Particulars Particular Acceleration due to Gravity Density of air



Value g ρair ρwater Vessel Particulars



Density of Water Particular



9.81 1.23



Default Value 9.81 1.23



Units m/s2 kg/m3



1025



1025



kg/m3



Value



Vessel Name



Units Ship 1



Principal Particulars Length Waterline (LWL)



LWL



116.74



m



Breadth Mean Draft (Working) Ship XCG (Longitudinal CG) - from Bow Displacement Wetted Surface Area1



B T Xcg Δ S



12.53 4.27 57.91 3403.75 1631.37



m m m MT m2



Wind Areas End projected wind area2



Ae



0



58.37 1631.37



m2



m2 As Side projected wind Area 845.44 Vessel Type (1 - for Normal shape, 2 - for Hull Dominated shape) 1 1 1 The default Wetted Surface Area, S, is approximated by formula S = 2.588 * √(Displacement * LWL). User can input a different figure if available 2 The End Projected wind Area should be input as zero if the environment is only in transverse direction



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



MOORING FORCES CALCULATION INPUTS- ENVIRONMENT



Particular Design Wind Speed Wind Angle (See Fig 1) - from 0 to 180 deg



Wind and Current Parameters Value Default Value Vw 25.72 θw 90



Current Speed Current Angle (See Fig 2) - from 0 to 180 deg Water Depth



Vc



1.5432



θc WD



0 13.72



Units 20 m/s degrees 0.5 m/s degrees m



Wind at angle θw



Current at angle θC



Fwd (Bow)



Aft (Stern)



Fwd (Bow)



Aft (Stern) 0 Degree



180 Degree



0 Degree 180 Degree



θW (deg) θ to be entered as the angle made by wind with the bow of the vessel. θ should be between 0 and 180 degrees (same for Port or Stbd wind)



Fig 1: Wind Angle



θC (deg) θ to be entered as the angle made by current with the bow of the vessel. θ should be between 0 and 180 degrees (same for Port or Stbd wind)



Fig 1: Current Angle



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



MOORING FORCES CALCULATION INPUTS- MOORING LINES Please input the mooring line properties in this worksheet. The maximum number of mooring lines possible is 16. The mooring pattern should be symmetrical about the vessel's midship Chock Coordinates on Ship (m) Bollard Coordinates at pier (m) Line No. (See Figs 1 & 2) (See Figs 1 & 2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16



Xch 0 4.88 11.58 21.34 96.93 106.68 110.95 118.87 80.47



Ych 0 1.52 2.74 4.88 6.1 5.33 4.88 3.05 6.1



Zch 6.4 5.79 5.49 4.72 2.9 3.05 3.2 3.2 2.9



Xbl -7.32 0 21.95 7.32 102.41 95.1 117.04 124.36 87.78



Ybl 8.23 8.23 8.23 8.23 8.23 8.23 8.23 8.23 8.23



Zbl 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74



Line Length from Bitt to Chock (m) (See Fig 2) l0 3.66 2.44 2.44 2.44 3.05 2.44 2.44 3.35 2.44



Young's modulus No. of rope parts of rope (GPa) E 1.378 1.378 1.378 1.378 1.378 1.378 1.378 1.378 1.378



n 3 3 3 3 3 3 3 3 3



Cross Sectional Area Minimum breaking of one rope Strength of one rope 2 (MT) (mm ) a MBSrope 1291 33.3 1291 33.3 1291 33.3 1291 33.3 1291 33.3 1291 33.3 1291 33.3 1291 33.3 1291 33.3



Z-axis Bitt



l0



Fyw (Wind) Mean Sea Level (MSL)



SHIP



Chock Z0h



Zbl



Y-axis Fyc (Current)



Mean Water Depth



Bollard



FIGURE 1: Sectional View of Pier and Ship l0 : Length of Mooring line from Bitt (on ship) to chock (on ship) Zch : Height (from MSL) of mooring line at chock Zbl : Height (from MSL) of mooring line at pier bollard



PIER



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



Xbl



Pier Bollard



Xch Y-axis



Ybl



Chock Bitt



Aft (Stern)



l0



Ych



COG



X-axis



Fwd (Bow) X=0



Mr (Total Yaw Moment) Fy (current + wind)



Fig 2: Plan View of a Typical Mooring Pattern (for reference only, not reflective of actual mooring pattern entered by user) Xch : Longitudinal distance of mooring line chock from vessel's bow Ych : Transverse distance of mooring line chock from vessel'' Centerline



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



Wind Forces and Yaw Moment Calculation* *



References: 1. DDS 582-1 Calculations for Mooring Systems, DDS-582-1-d(1) 1



FXW = 1/2 *



2 given in by:Longitudinal CXW ρair*VWWindload *AE (Windis Force



FYW = 1/2 *



CYW ρair*VW2*AS



Table 1: CXW vs Wind Angle



0.9



direction)



0.8 0.7



(Wind Force in Transverse direction)



FXYW = 1/2 * CXYW ρair*VW2*AS * LWL (Wind Yaw Moment) ρair = Density of Air, Vw = Wind Speed , AE = End projected Wind Ares, AS = Side Projected Wind Area C xw = Longitudinal Wind Force Coefficient (See Table 1), C yw = Lateral Wind Force Coefficient (See Table 2), C xyw = Wind Yaw Moment Coefficient (See Table 3)



0.6 0.5 0.4 0.3 0.2



Particulars Length of Waterline End projected wind area



Basic Parameters Notation HULL LWL Ae



0.1



Value



Units 116.74 0



m m2 m2



Side projected Wind Area Design Wind Speed



As Vw



845.44 25.72



Density of air Wind Angle Ship Type ( 1 - Normal, 2 - Hull dominated)



ρair θw



1.23 90 1



-0.1 0 -0.2



CXW CYW CXYW



30



60



90



120



150



Lateral Wind Force Total Factored Windage Area of Hull in Lateral Direction



0 30



0.9 0.78



0.45 0.38



60 90 120 150 180



0.45 0 -0.45 -0.78 -0.9



0.23 0 -0.23 -0.38 -0.45



Cxw(Hull dominated Ships)



180



Wind Angle (deg) --->



-0.4



m/s kg/m3



-0.5



degrees



-0.7



-0.6 -0.8 -0.9 -1



0 See Table 1 1 See Table 2 -0.037 See Table 3



Cyw



CYW Angle (deg) CYW 0 30 60



Table 2: CyW vs Wind Angle



1.1



Longitudinal Wind Force



Chull



-0.3



Wind Force Coefficients Longitudinal Wind Force Coefficient Lateral Wind Force Coefficient Wind Yaw Moment Coefficient



Cxw (Normal Ships)



0



Angle (deg)



CXW Cnormal



WINDLOAD FXW = 1/2 *Cxw * ρair*Vw2*AE FYW = 1/2 * Cyw * ρair*Vw2*AS MW = 1/2 * Cxyw * ρair*Vw2*AS * LWL



1



0.00 MT



0.9



35.06 MT -151.44 MT-m



0.8 0.7 0.6



0 0.48 0.87



90



1



120 150 180



0.87 0.48 0



Cyw



0.5 0.4 0.3 0.2



Wind Angle (deg) --->



0.1 0 0



30



60



90



120



150



180



Table 3: CxyW vs Wind Angle



Cxyw



0.04



Wind Angle (deg) ---> 0



-0.06



-0.16



30



60



90



120



150



180



CXYW Angle (deg) CXYW 0 10 30 45 60 90 120 135 150 180



0 0.023 0.054 0.063 0.054 -0.037 -0.14 -0.155 -0.14 0



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



Current Forces and Yaw Moment Calculation* *



References: 1. DDS 582-1 Calculations for Mooring Systems, DDS-582-1-d(2)



Cxca



Current Moments are given FXC = 1/2 * ρwater*VC2*B *( CXCA * Forces S /LWLand + CXCB * T) (Current Forceby: in Longitudinal direction) FYC = 1/2 * CYC ρwater*



VC2



CXCA



Table 1: CXCA vs Wind Angle



Angle (deg)



0.4



* LWL * T (Current Force in Transverse direction)



FXYC = 1/2 * CXYC ρair*VC2 * LWL2 * T (Current Yaw Moment) ρwater = Density of Water, VC = Current Speed, CXCA = Longitudinal Current Skin Friction Coefficient (Table 1), CXCB = Longitudinal Current Drag Coefficient C YC = Lateral Current Force Coefficient (See Table 2), C XYC = Current Yaw Moment Coefficient (See Table 3), S = Wetted Surface Area of Hull



0.3



0.2



Note 1: C XCB is given by formula C XCB = C YC * cos 2 θC



Cxca



0 30



0.34 0.27



60 90 120 150 180



0.09 0 -0.085 -0.27 -0.34



0.1



Basic Parameters Particulars Length of Waterline Breadth Draft Water Depth Wetted Surface Area Design Current Speed Density of water Current Angle Ratio of Water Depth to Draft WD/T



Notation



Value HULL LWL B T WD S VC



ρwater θC WD/T Current Force Coefficients



Units 0



116.74 12.53 4.27 13.72 1631.37 1.5432 1025 0 3.22



m m m m m2 m/s kg/m3



-0.4



Longitudinal Current Drag Coefficient Current Yaw Moment Coefficient



CXCB CXYC



2 0.0000 CYC * cos θC 0.0000 See Table 3



4.2 4.1 4 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0



Current Yaw Moment



120



150



180



-0.3



0.3400 See Table 1 0.0000 See Table 2



Lateral Current Force



90



-0.2



CXCA CYC



FYC = 1/2 *CYC*ρwater*VC2*LWL*T) FXYC = 1/2 *CXYC*ρwater*VC2*LWL2*T)



60



-0.1



Longitudinal Current Skin Friction Coefficient Lateral Current Force Coefficient



Longitudinal Current Force



30



Wind Angle (deg) --->



degrees



WINDLOAD FXC = 1/2 *ρwater*VC2*B*(CXCA*S/LWL + CXCB*T)



Cxca 0



7.41 MT 0.00 MT 0.00 MT-m



Table 2: CYC vs Wind Angle



Angle (deg) 0 30 60 70



Cyc(WD/T=1.05)



90



3.95



3.5



2.8



1.95



1.5



1.2



0.78



Cyc(WD/T=1.10)



110 120 150 180



3.7 2.8 1.8 0



3.1 2.55 1.35 0



2.55 2.25 1.15 0



1.8 1.65 0.9 0



1.38 1.25 0.6 0



1.1 0.95 0.48 0



0.68 0.6 0.3 0



Cyc(WD/T=1.20) Cyc(WD/T=1.50) Cyc(WD/T=2.00) Cyc(WD/T=3.00) Cyc(WD/T=6.00)



Wind Angle (deg) --->



0



30



60



90



120



0.5



150



180



Table 3: CXYC vs Wind Angle



0.4



Angle (deg)



0.3 0.2 Series1 Series2



0.1



Series3 0



Series4 0



30



60



-0.1



90



120



150



180



Series5 Series6 Series7



-0.2 -0.3



Wind Angle (deg) ---> -0.4 -0.5



WD/T = 1.05 WD/T = 1.10 0 0 1.8 1.35 2.8 2.55 3.7 3.1



CYC WD/T = 1.20 WD/T = 1.50 WD/T = 2.00 WD/T = 3.00 WD/T = 6.00 0 0 0 0 0 1.15 0.9 0.6 0.48 0.3 2.25 1.65 1.25 0.95 0.6 2.55 1.8 1.38 1.1 0.68



0 30 45 60 80 90 120 140 150 180



WD/T = 1.05 WD/T = 1.10 0 0 0.37 0.3 0.325 0.27 0.19 0.15 -0.02 -0.03 -0.12 -0.1 -0.315 -0.3 -0.375 -0.345 -0.36 -0.33 0 0



CXYC WD/T = 1.20 WD/T = 1.50 WD/T = 2.00 WD/T = 3.00 WD/T = 6.00 0 0 0 0 0 0.23 0.15 0.11 0.065 0.043 0.24 0.16 0.125 0.08 0.04 0.16 0.125 0.1 0.06 0.03 0 0.01 0.02 0 0 -0.075 -0.05 -0.035 -0.03 -0.02 -0.265 -0.225 -0.18 -0.115 -0.06 -0.31 -0.26 -0.195 -0.12 -0.058 -0.288 -0.23 -0.17 -0.105 -0.05 0 0 0 0 0



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



Final Total Forces and Moment *



References: 1. DDS 582-1 Calculations for Mooring Systems, DDS-582-1-d(3)



Longitudinal Wind + Current Force Lateral Wind + Current Force Total Yaw Moment



FINAL FORCES AND MOMENTS FX = FXC + FXW FY = FYC + FYW Mr = MC + MW - 0.48 * LWL * FX



7.41 MT 35.06 MT -566.40 MT-m



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



MOORING FORCES CALCULATION - MOORING LINE FORCES References: 1. DDS 582-1 Calculations for Mooring Systems, DDS-582-1-e *



FY (kN) Mr (kN-m) Xcg(m)



*Note: Factor of Safety should be more than 9 for Normal environment, and more than 3 for extreme environment



Chock Coordinates on Ship (m) Bollard Coordinates at pier (m) Line No. See Fig 1 & Fig 2 See Fig 1 & Fig 2



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16



Xch 0 4.88 11.58 21.34 96.93 106.68 110.95 118.87 80.47



Ych 0 1.52 2.74 4.88 6.1 5.33 4.88 3.05 6.1



Zch 6.4 5.79 5.49 4.72 2.9 3.05 3.2 3.2 2.9



Xbl -7.32 0 21.95 7.32 102.41 95.1 117.04 124.36 87.78



Ybl 8.23 8.23 8.23 8.23 8.23 8.23 8.23 8.23 8.23



Zbl 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74



l1 = √{(Xch - Xbl)2 + 2



(Ych - Ybl) } See Fig 2 l1 11.01 8.3 11.73 14.41 5.88 11.94 6.95 7.55 7.61



ΔZi = Zch - Zbl See Fig 1 ΔZi 3.66 3.05 2.75 1.98 0.16 0.31 0.46 0.46 0.16



Cross Sectional Cross Sectional Minimum Minimum No. of Area of one Area of breaking breaking Strength rope rope mooring line Strength of one of Mooring Line parts rope (MT) (MT) (mm2) (mm2) a n ai = n x a MBSrope MBS = MBSrope x n 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9 1291 3 3873 33.3 99.9



Young's modulus of rope (GPa)



cos θi = (Ybl Ych)/l1 See Fig 2



φi = tan (ΔZi/l1) See Fig 1



cos φi



Ei 1.378 1.378 1.378 1.378 1.378 1.378 1.378 1.378 1.378



cos θi 0.748 0.808 0.468 0.232 0.362 0.243 0.482 0.686 0.280



φi 18.388 20.177 13.194 7.824 1.559 1.487 3.787 3.487 1.204



cos φi 0.94894 0.93863 0.97360 0.99069 0.99963 0.99966 0.99782 0.99815 0.99978



-1



Line Length from Bitt to Chock (m) See Fig 2 l0 3.66 2.44 2.44 2.44 3.05 2.44 2.44 3.35 2.44



343.95 a (kN/m) -5556.40 b (kN) 57.91 c (kN-m)



1910.042 δy (m) =



0.266 2



117866.463 δy = (Fy*c - (Mr + Fy*Xcg)*b)/(ac-b ) 12175733.665 γ (radian) -0.001399758 γ = (Fy*b - (Mr + Fy*Xcg)*a)/(b2-ac)



Li = l0 + l1/cos φi (m)



ki = ai * Ei/Li (kN/m)



kyi = ki * cosθi*cosφi (kN/m)



kyi * Xch (kN)



kyi * Xch (kN-m)



Li 15.262 11.283 14.488 16.985 8.932 14.384 9.405 10.914 10.052



ki 349.682 473.027 368.372 314.211 597.502 371.036 567.451 489.004 530.955



kyi 248.042 358.943 167.858 72.367 216.362 90.087 272.922 334.881 148.579



kyi * Xch 0.000 1751.642 1943.798 1544.311 20971.968 9610.515 30280.742 39807.348 11956.139



kyi * Xch 0.000 8548.012 22509.185 32955.599 2032812.860 1025249.783 3359648.291 4731899.415 962110.519



a = 1178.54



b = 66102.98



2



2



c = 6481723.73



Fyi = kyi *(δy +



Ti = Fyi /(cosθi *



Xch*γ) (MT)



cosφi) (MT)



FSi (Factor of Safety) = MBS/Ti



Fyi 6.737 9.499 4.282 1.745 2.884 1.076 3.092 3.416 2.330



Ti 9.498 12.519 9.397 7.578 7.965 4.430 6.429 4.988 8.325



FSi 10.518 7.980 10.631 13.183 12.542 22.551 15.538 20.028 12.000



MOORING FORCES CALCULATOR (PORT/STBD ON QUAY) www.thenavalarch.com



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